Analysis of the parameter estimate error when algebraic differentiators are used in the presence of disturbances

Abstract

The use of algebraic differentiators in the context of asymptotic continuous-time parameter estimation is discussed. The estimation problem is analyzed within a least squares optimization context. Bounds for the error stemming from high frequency disturbances and the approximation of the derivatives are derived. It is shown that with higher frequencies the error stemming from the disturbances decreases and that the filter parameters can be used to adjust the convergence of this error to zero. An observer with assignable error dynamics for the online estimation is also proposed. A simulation is carried out to evaluate the results and compare the proposed observer with the recursive solution of the least squares problem.